0
Research Papers

Approximation of Cylindrical Surfaces With Deployable Bennett Networks

[+] Author and Article Information
Shengnan Lu

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: lvshengnan5@gmail.com

Dimiter Zlatanov

PMAR Robotics,
University of Genoa,
Genoa 16145, Italy
e-mail: zlatanov@dimec.unige.it

Xilun Ding

Robotics Institute,
Beihang University,
Beijing 100191, China
e-mail: xlding@buaa.edu.cn

Manuscript received October 17, 2016; final manuscript received January 10, 2017; published online March 9, 2017. Assoc. Editor: Venkat Krovi.

J. Mechanisms Robotics 9(2), 021001 (Mar 09, 2017) (6 pages) Paper No: JMR-16-1322; doi: 10.1115/1.4035801 History: Received October 17, 2016; Revised January 10, 2017

This paper presents a one-degree-of-freedom network of Bennett linkages which can be deployed to approximate a cylindrical surface. The geometry of the unit mechanism is parameterized and its position kinematics is solved. The influence of the geometric parameters on the deployed shape is examined. Further kinematic analysis isolates those Bennett geometries for which a cylindrical network can be constructed. The procedure for connecting the unit mechanisms in a deployable cylinder is described in detail and used to gain insight into, and formulate some general guidelines for, the design of linkage networks which unfold as curved surfaces. Case studies of deployable structures in the shape of circular and elliptical cylinders are presented. Modeling and simulation validate the proposed approach.

Copyright © 2017 by ASME
Topics: Linkages , Shapes
Your Session has timed out. Please sign back in to continue.

References

Escrig, F. , Valcarcel, J. P. , and Sanchez, J. , 1996, “ Deployable Cover on a Swimming Pool in Seville,” Bull. Int. Assoc. Shell Spat. Struct., 37(1), pp. 39–70.
Zhao, J. S. , Wang, J. Y. , Chu, F. L. , Feng, Z. J. , and Dai, J. S. , 2012, “ Mechanism Synthesis of a Foldable Stair,” ASME J. Mech. Rob., 4(1), p. 014502. [CrossRef]
Durand, G. , Sauvage, M. , Bonnet, A. , Rodriguez, L. , Ronayette, S. , Chanial, P. , Scola, L. , Révéret, V. , Aussel, H. , Carty, M. , Durand, M. , Durand, L. , Tremblin, P. , Pantin, E. , Berthe, M. , Martignac, J. , Motte, F. , Talvard, M. , Minier, V. , and Bultel, P. , 2014, “ TALC: A New Deployable Concept for a 20-m Far-Infrared Space Telescope,” SPIE Astronomical Telescopes+ Instrumentation, International Society for Optics and Photonics, Montreal, Quebec, Canada, June 22, p. 91431A.
Maden, F. , Korkmaz, K. , and Akgün, Y. , 2011, “ A Review of Planar Scissor Structural Mechanisms: Geometric Principles and Design Methods,” Archit. Sci. Rev., 54(3), pp. 246–257. [CrossRef]
Zhao, J. S. , Chu, F. L. , and Feng, Z. J. , 2009, “ The Mechanism Theory and Application of Deployable Structures Based on SLE,” Mech. Mach. Theory, 44(2), pp. 324–335. [CrossRef]
O'brian, E. D. , and Phelan, C. , 1984, “ Folding Structure Employing a Sarrus Linkage,” U.S. Patent No. 4,437,413.
Lu, S. N. , Zlatanov, D. , Ding, X. L. , Molfino, R. , and Zoppi, M. , 2016, “ Novel Deployable Mechanisms With Decoupled Degrees-of-Freedom,” ASME J. Mech. Rob., 8(2), p. 021008. [CrossRef]
Deng, Z. , Huang, H. , Li, B. , and Liu, R. , 2011, “ Synthesis of Deployable/Foldable Single Loop Mechanisms With Revolute Joints,” ASME J. Mech. Rob., 3(3), p. 031006. [CrossRef]
Li, B. , Huang, H. , and Deng, Z. , 2016, “ Mobility Analysis of Symmetric Deployable Mechanisms Involved in a Coplanar 2-Twist Screw System,” ASME J. Mech. Rob., 8(1), p. 011007. [CrossRef]
Chen, Y. , and You, Z. , 2008, “ On Mobile Assemblies of Bennett Linkages,” Proc. R. Soc. London, Ser. A, 464(2093), pp. 1275–1293. [CrossRef]
Chen, Y. , 2003, “ Design of Structural Mechanisms,” Ph.D. thesis, University of Oxford, Oxford, UK.
Liu, S. Y. , and Chen, Y. , 2009, “ Myard Linkage and Its Mobile Assemblies,” Mech. Mach. Theory, 44(10), pp. 1950–1963. [CrossRef]
Qi, X. Z. , Deng, Z. Q. , Li, B. , Liu, R. Q. , and Guo, H. W. , 2013, “ Design and Optimization of Large Deployable Mechanism Constructed by Myard Linkages,” CEAS Space J., 5(3–4), pp. 147–155. [CrossRef]
Lu, S. N. , Zlatanov, D. , Ding, X. L. , Zoppi, M. , and Guest, S. D. , 2015, “ A Network of Type III Bricard Linkages,” ASME Paper No. DETC2015-47139.
Chu, Z. R. , Deng, Z. Q. , Qi, X. Z. , and Li, B. , 2014, “ Modeling and Analysis of a Large Deployable Antenna Structure,” Acta Astronaut., 95, pp. 51–60. [CrossRef]
Rahmat-Samii, Y. , Huang, J. , Lopez, B. , Lou, M. , Im, E. , Durden, S. L. , and Bahadori, K. , 2005, “ Advanced Precipitation Radar Antenna: Array-Fed Offset Membrane Cylindrical Reflector Antenna,” IEEE Trans. Antennas Propag., 53(8), pp. 2503–2515. [CrossRef]
Hoberman, C. , and Davis, M. , 2010, “ Synchronized Four-Bar Linkages,” U.S. Patent No. 7,644,721.
Hoberman, C. , 2006, “ Transformation in Architecture and Design,” Transportable Environments 3, Vol. 3, Taylor & Francis, New York, pp. 70–73.
Lu, S. N. , Zlatanov, D. , and Ding, X. L. , 2016, “ Approximation of Cylindrical Surfaces With Deployable Bennett Networks,” ASME Paper No. DETC2016-59817.
Bennett, G. , 1903, “ A New (Four-Piece Skew) Mechanism,” Engineering, 76, pp. 777–778.
Waldron, K. , 1979, “ Overconstrained Linkages,” Environ. Plann. B, 6(4), pp. 393–402. [CrossRef]
Phillips, J. , 2007, Freedom in Machinery, Vol. 1, Cambridge University Press, New York.

Figures

Grahic Jump Location
Fig. 1

The Bennett linkage and its geometric description [22]

Grahic Jump Location
Fig. 2

An alternative form of the Bennett linkage

Grahic Jump Location
Fig. 3

The two perpendicular planes

Grahic Jump Location
Fig. 4

Two bundle-folding realizations of the same Bennett

Grahic Jump Location
Fig. 5

Description of two revolute axes on a rigid segment

Grahic Jump Location
Fig. 6

Relationship among mechanism angles

Grahic Jump Location
Fig. 7

Coordinate system of the Bennett linkage

Grahic Jump Location
Fig. 8

Projection of the Bennett linkage on Oyz

Grahic Jump Location
Fig. 9

Influence of γ on |M2M4|

Grahic Jump Location
Fig. 10

Influence of δ on φ

Grahic Jump Location
Fig. 11

Two Bennets connected by a scissor linkage

Grahic Jump Location
Fig. 12

Tessellation of the Bennett network

Grahic Jump Location
Fig. 13

Mesh of a cylindrical surface

Grahic Jump Location
Fig. 14

Segmenting the circle to obtain Bennett dimensions

Grahic Jump Location
Fig. 15

Kinematic simulation: deployment (a)–(c) of a circular half-cylinder

Grahic Jump Location
Fig. 16

Segmentation of the ellipse

Grahic Jump Location
Fig. 17

Kinematic simulation: deployment (a)–(d) of an elliptical half-cylinder

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In